TY - JOUR
T1 - A characterization of duality through section/projection correspondence in the finite dimensional setting
AU - Milman, Vitali D.
AU - Segal, Alexander
AU - Slomka, Boaz A.
N1 - Funding Information:
✩ The first and second named authors were partially supported by the ISF grant No. 387/09 and the third named author was partially supported by the ISF grant No. 865/07. * Corresponding author. Fax: +972 77 4220101. E-mail addresses: [email protected] (V.D. Milman), [email protected] (A. Segal), [email protected], [email protected] (B.A. Slomka).
PY - 2011/12/1
Y1 - 2011/12/1
N2 - In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.
AB - In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.
KW - Duality
KW - Polar convex sets
KW - Section-projection correspondence
UR - http://www.scopus.com/inward/record.url?scp=80053276332&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2011.08.007
DO - 10.1016/j.jfa.2011.08.007
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AN - SCOPUS:80053276332
SN - 0022-1236
VL - 261
SP - 3366
EP - 3389
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 11
ER -